Mixed Fractions

Mixed fractions, also known as mixed numbers, are a combination of a whole number and a fraction. They are typically used to represent quantities that are larger than one whole but less than two wholes.

Representation of Mixed Fractions

Mixed fractions are represented in the form of a whole number followed by a proper fraction. For example, 2 3/4 is a mixed fraction, where 2 is the whole number and 3/4 is the proper fraction.

Conversion from Mixed Fractions to Improper Fractions

To perform mathematical operations with mixed fractions, it is often helpful to convert them into improper fractions. The following steps can be followed to convert a mixed fraction to an improper fraction:
1. Multiply the whole number by the denominator of the fraction.
2. Add the result to the numerator.
3. Write the sum obtained in step 2 over the denominator to obtain the improper fraction.

For example, to convert 2 3/4 to an improper fraction:
1. Multiply 2 (whole number) by 4 (denominator) to get 8.
2. Add 8 to 3 (numerator) to get 11.
3. Write 11/4 as the improper fraction.

Operations with Mixed Fractions

Operations such as addition, subtraction, multiplication, and division can be performed with mixed fractions. However, it is usually easier to convert mixed fractions into improper fractions before performing these operations.

For example, to add 2 3/4 and 1 2/3:
1. Convert both mixed fractions to improper fractions.
2. Add the numerators and write the sum over the common denominator.

Conversion from Mixed Fractions to Decimals

Mixed fractions can also be converted into decimals. To convert a mixed fraction to a decimal, the following steps can be followed:
1. Convert the fraction part to a decimal by dividing the numerator by the denominator.
2. Add the obtained decimal to the whole number part.

For example, to convert 2 3/4 to a decimal:
1. Divide 3 by 4 to get 0.75.
2. Add 2 (whole number) to 0.75 to get 2.75 as the decimal representation.

Class 7 Math

In Class 7 Math, students learn about various concepts including fractions, decimals, and mixed fractions. They understand the representation and conversion of mixed fractions, perform operations with them, and convert them into decimals. These concepts lay the foundation for more advanced mathematical topics in higher grades. It is important for students to practice solving problems involving mixed fractions to develop a strong understanding of these concepts.